Electronic structure of (13,0) and (15,0) zig-zag single wall carbon nanotubes (SWCNTs) under uniaxial strain are studied using order N, tight binding molecular dynamic (O(N) TBMD) simulation code designed by Dereli et.al. Total energy and Fermi energy levels are obtained as functions of strain. Band gap calculated from behavior of electronic density of states near fermi energy level for each strain values. The energy band gaps of these carbon nanotubes are modified by compressive and tensile strain and they exhibit semiconductor - metal and metal - semiconductor transitions.